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Considering an assertion that the fundamental difference between different ‘types’ of electromagnetic waves is frequency/wavelength, and larger antennas are needed for longer wavelengths, if my eyes were larger proportional to the difference in wavelength between visible light waves and radio waves, would they see radio waves?

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No. But the reasons are biological, not physical. Your eyes work by the interaction of electromagnetic radiation with certain molecules ( rhodopsin which consists of the protein opsin linked to 11-cis-retinal, a prosthetic group.)

These molecules are tuned to detect light of particular wavelengths. But they couldn't be tuned to detect radio-waves, since radio waves are much larger than molecules. To detect radio waves, you need an antenna, not a light sensitive molecule.

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Yes, and the reasons are both physical and biological.

  • Our eyes use molecules that can be excited by electromagnetic visible light waves (wavelength 0.4 to 0.7 microns roughly) and those excitations can then be converted to other molecular signals and eventually depolarization of nerve cell membranes ("neurons firing").

  • Snake eye-pits use molecules that can be excited by electromagnetic thermal infrared light waves (10 to 30 microns roughly) and those excitations can then be converted to other molecular signals and eventually depolarization of nerve cell membranes ("neurons firing").

  • Our eyes use lenses to produce inverted images on our retinas and use neural nets within the retina and then the brain to convert them to useful information.

  • Snakes use pinhole cameras to produce inverted images on their eye-pit "retinas" and use neural nets within the retina and then the brain to convert them to useful information.

snake eye-pits as pinhole cameras

As far as I know there are currently no known organisms that "see" radio waves. However, there are certainly molecules that could be inefficiently stimulated by radio waves. GHz frequencies will warm water and so a "radio retina" could work off of tiny temperature shifts just like the snake's eye-pit "retina" does.

It is also conceivable that your giant eyes could eventually evolve molecules with quantum resonances in the few x 100 cm-1 to few x 1000 cm-1 range (30 to 3 microns) just like those hypothesized in the Vibration theory of olfaction (See also Status of the Vibrational Theory of Olfaction and New evidence for the vibration theory of smell and Differential Odour Coding of Isotopomers in the Honeybee Brain and An Update on Vibrational Theories of Smell) These molecules could easily have dipole moments allowing them to be excited directly by electromagnetic radiation, or indirectly by thermal excitation, and if directly, then "color" vision would be facilitated by molecules with different resonant frequencies just like in the theory of olfaction.

However you'd need either reflective optics (a shiny concave surface instead of a lens) or a thin fresnel lens or compound eye using lenslets based on water's attenuation length of millimeters at some near infrared wavelengths.

But most people would call this wavelength range infrared, not radio, so it doesn't count.

Summary

If you made a giant eyeball say ten meters in diameter, the lens could focus radio waves but only at certain thicknesses and wavelengths. The figure below shows that in the long wavelength limit the real index of refraction $n$ of water is about 9 and the imaginary part $k$ drops with longer wavelength.

Of course if the lens were made of mostly nonpolar (or less-polar) molecules like some proteins or fats, then they would have to be a lot thicker (real index circa 1.5) more like optical lens shapes, but hopefully the absorption $k$ would be lower too.

Using radio wavelengths you'd probably have to use the thermal effect; again like the snake's eye-pit "retina" you'd have to use water or some even more polar molecules to absorb the radio waves locally and convert their energy to a tiny increase in temperature.

If the radio waves were really really strong, your retina might respond to temperature changes, but this would not be efficient.


Source: Ms. Thesis of Mark Lee Mesenbrink (1996); Complex Indices of Refraction for Water and Ice from Visible to Long Wavelengths

Figure 3.9. Complex indices of refraction for water in the microwave/ radiowave region.

Figure 3.9. Complex indices of refraction for water in the microwave/ radiowave region. - Calculated n (top) and k (bottom); e Schwan et al. [1976] at 25 0C, uncertainty of ±1% for n and ±3% for k; E Sheppard [1973] at 40C, uncertainty of ±1% for n and ±3% for k; 0?Grant and Sheppard [19741 at 40C, uncertainty of ±1% for n and ±3% for k.

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